I think you will need a keel, not necessarily so much to avoid making excessive leeway, but to counteract the heeling effect of the non-scale wind, and give sufficient righting moment. However, if the ballast was sheet lead on a flat barge floor , ie as low down as it's possible to get it inside the boat, it might work, provided the wind is very steady and not gusting. I've sailed sailing canoes, 11' and 17' long with no keels at all and really quite small leeboards are quite enough to get the boats running straight - though you do need to get a bit of speed up to get a reasonable water flow over them before you can point up much.
On balance, as winds do gust, I think you would need outside ballast.